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Mirrors > Home > ILE Home > Th. List > 5t2e10 | GIF version |
Description: 5 times 2 equals 10. (Contributed by NM, 5-Feb-2007.) (Revised by AV, 4-Sep-2021.) |
Ref | Expression |
---|---|
5t2e10 | ⊢ (5 · 2) = ;10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 5nn0 9115 | . 2 ⊢ 5 ∈ ℕ0 | |
2 | 1nn0 9111 | . 2 ⊢ 1 ∈ ℕ0 | |
3 | df-2 8897 | . 2 ⊢ 2 = (1 + 1) | |
4 | 5cn 8918 | . . 3 ⊢ 5 ∈ ℂ | |
5 | 4 | mulid1i 7882 | . 2 ⊢ (5 · 1) = 5 |
6 | 5p5e10 9370 | . 2 ⊢ (5 + 5) = ;10 | |
7 | 1, 2, 3, 5, 6 | 4t3lem 9396 | 1 ⊢ (5 · 2) = ;10 |
Colors of variables: wff set class |
Syntax hints: = wceq 1335 (class class class)co 5826 0cc0 7734 1c1 7735 · cmul 7739 2c2 8889 5c5 8892 ;cdc 9300 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-sep 4084 ax-cnex 7825 ax-resscn 7826 ax-1cn 7827 ax-1re 7828 ax-icn 7829 ax-addcl 7830 ax-addrcl 7831 ax-mulcl 7832 ax-mulcom 7835 ax-addass 7836 ax-mulass 7837 ax-distr 7838 ax-1rid 7841 ax-0id 7842 ax-rnegex 7843 ax-cnre 7845 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-int 3810 df-br 3968 df-iota 5137 df-fv 5180 df-ov 5829 df-inn 8839 df-2 8897 df-3 8898 df-4 8899 df-5 8900 df-6 8901 df-7 8902 df-8 8903 df-9 8904 df-n0 9096 df-dec 9301 |
This theorem is referenced by: 5t3e15 9400 ex-fac 13375 |
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